A case-study of the Stokes geometry in the large is  given for some concrete examples of WKB type operators that admit  infinitely many phases. In all the examples discussed in this article  virtual turning points and new Stokes curves emanating from  them neatly resolve the trouble we encounter. Some computerassisted  study of the configuration of the steepest descent paths  is employed to show that the introduction of new Stokes curves is  reasonable and appropriate to obtain the complete Stokes geometry